6.4 Velocity addition
Subject:
“When in […] u is eliminated, we get
u=
uʼ + v
.
uʼv
1+ 2
c
This is Einstein’s relativistic law of velocity addition.”
Deficiencies:
The equation tells us how the physical quantity velocity transforms when
the reference frame is changed. There are corresponding laws for the
transformation of length and time intervals, of energy and momentum, of
electric and magnetic field strength, and others, but only in the case of the
velocity one refers to “addition“, instead of transformation. This may make
the students believe that the case of velocity is basically different from the
other transformations.
One should also remember that the term “addition” is reserved for the wellknown mathematical operation.
When calling the above equation “velocity-addition formula” the students
may believe that it is principally incorrect to add velocities in the normal
way. Since normal mathematical addition can result in a velocity greater
than c, the addition would not be allowed. However, this argument is not
correct. One may and one must add up velocities, whatever the result of the
operation is, when for instance, one wants to calculate an average velocity
from many single velocities.
Origin:
Einstein himself called the formula addition-law [1]. The name is suggestive, since for small velocities the equation reduces to a simple mathematical addition.
Disposal:
Call the above equation transformation law instead of addition law.
[1] A. Einstein: Grundzüge der Relativitätstheorie, Akademieverlag Berlin,
1970, S. 39.
Friedrich Herrmann